The Agile Manifesto emphasizes valuing individuals and interactions over processes and tools, working software over comprehensive documentation, customer collaboration over contract negotiation, and responding to change over following a plan. Non-relational databases like MongoDB offer flexible schemas, allowing for less upfront planning and more focus on getting the application working, as well as polymorphic data that can adapt to changing requirements without explicit schema changes. This flexibility enables developers to respond quickly to change and scale their database horizontally, making it easier to handle increased loads and costs associated with scaling relational databases.